Ultimate Texas Hold 'Em

Introduction

Ultimate Texas Hold'em® is a poker-based casino game in which the player may make one raise at any time during the course of the hand. The earlier the raise is made the higher it may be. Unlike other poker-based games, raises made after the ante still have action, even if the dealer doesn't open. This game was invented by Roger Snow of . The same base game is also distributed by Galaxy Gaming under the name Heads Up Hold 'Em.

ULTIMATE TEXAS HOLD ’EM® is a registered trademark of Bally Gaming, Inc. and is used with permission on this website.

Rules

Following are the standard rules as played in the United States. There is a variant played in Auckland, New Zealand, I address following the standard rules.

The game is played with a single ordinary 52-card deck.

The player must make an equal bet on both the Ante and Blind, and can also make an optional Trips bet.

Two cards are dealt face down to the player and dealer. The player may look at his own cards.

The player can check or make a Play bet equal to three or four times the Ante.

The dealer turns over three community cards.

If the player previously checked, then he may make a Play bet equal to two times his Ante. If the player already made a Play bet, then he may not bet further.

Two final community cards are turned over.

If the player previously checked twice, then he must either make a Play bet equal to exactly his Ante, or fold, losing both his Ante and Blind bets. If the player already raised he may not bet further.

The player and dealer will both make the best possible hand using any combination of their own two cards and the five community cards.*

The dealer will need at least a pair to open.

The following table shows how the Blind, Ante, and Play bets are scored, according to who wins, and whether the dealer opens.

Scoring Rules

Winner

Dealer Opens

Blind

Ante

Play

Player

Yes

Win

Win

Win

Player

No

Win

Push

Win

Dealer

Yes

Lose

Lose

Lose

Dealer

No

Lose

Push

Lose

Tie

Yes or No

Push

Push

Push

Winning Ante and Play bets pay 1 to 1. Winning Blind bets pay according to the following pay table.

Blind Bet Pay Table

Player Hand

Pays

Royal flush

500 to 1

Straight flush

50 to 1

Four of a kind

10 to 1

Full house

3 to 1

Flush

3 to 2

Straight

1 to 1

All other

Push

The Trips bet will pay according to the poker value of the player's hand regardless of the value of the dealer's hand, according to one of the Trip bet pay tables below.

Notes:

* While the standard rules let both player and dealer use any five cards to make their best poker hand, in Auckland, New Zeland, both sides must make use of both hole cards and three of the five community cards. An analysis of the game under this rule can be found in my page on Ultimate Texas Hold 'Em -- Auckland Variant.

Analysis

There are 52 possible outcomes of each hand. The table below shows the probability of each and the contribution to the total return, assuming optimal strategy. A 4X raise is referred to as a "large raise," a 2X raise as "medium," and 1x as "small."

Return TableExpand

Raise

DealerQualifies

Player Hand

Winner

Pays

Combinations

Probability

Return

Large

Yes

Less than straight

Player

5

3,671,050,165,880

0.131987

0.659933

Large

Yes

Straight

Player

6

246,174,692,160

0.008851

0.053105

Large

Yes

Flush

Player

6.5

241,047,929,080

0.008666

0.056332

Large

Yes

Full house

Player

8

295,405,180,920

0.010621

0.084966

Large

Yes

Four of a kind

Player

15

23,008,208,760

0.000827

0.012408

Large

Yes

Straight flush

Player

55

1,818,135,760

0.000065

0.003595

Large

Yes

Royal flush

Player

505

596,356,920

0.000021

0.010828

Large

No

Less than straight

Player

4

1,556,797,035,840

0.055972

0.223888

Large

No

Straight

Player

5

81,416,649,960

0.002927

0.014636

Large

No

Flush

Player

5.5

50,874,988,680

0.001829

0.010060

Large

No

Full house

Player

7

0

0.000000

0.000000

Large

No

Four of a kind

Player

14

0

0.000000

0.000000

Large

No

Straight flush

Player

54

229,686,840

0.000008

0.000446

Large

No

Royal flush

Player

504

90,386,280

0.000003

0.001638

Large

0

Push

0

285,142,270,600

0.010252

0.000000

Large

Yes

Dealer

-6

3,931,554,359,920

0.141353

-0.848116

Large

No

Dealer

-5

102,655,952,400

0.003691

-0.018454

Medium

Yes

Less than straight

Player

3

2,114,839,654,764

0.076036

0.228107

Medium

Yes

Straight

Player

4

133,100,158,992

0.004785

0.019142

Medium

Yes

Flush

Player

4.5

152,618,008,784

0.005487

0.024692

Medium

Yes

Full house

Player

6

289,401,836,880

0.010405

0.062430

Medium

Yes

Four of a kind

Player

13

18,537,793,620

0.000666

0.008664

Medium

Yes

Straight flush

Player

53

2,704,129,504

0.000097

0.005153

Medium

Yes

Royal flush

Player

503

112,333,500

0.000004

0.002031

Medium

No

Less than straight

Player

2

1,083,763,469,592

0.038965

0.077930

Medium

No

Straight

Player

3

45,053,788,356

0.001620

0.004860

Medium

No

Flush

Player

3.5

38,820,798,396

0.001396

0.004885

Medium

No

Full house

Player

5

0

0.000000

0.000000

Medium

No

Four of a kind

Player

12

0

0.000000

0.000000

Medium

No

Straight flush

Player

52

358,131,456

0.000013

0.000670

Medium

No

Royal flush

Player

502

8,830,620

0.000000

0.000159

Medium

Push

0

191,611,691,060

0.006889

0.000000

Medium

Yes

Dealer

-4

1,841,155,221,088

0.066196

-0.264783

Medium

No

Dealer

-3

7,978,353,108

0.000287

-0.000861

Small

Yes

Less than straight

Player

2

1,375,033,295,072

0.049437

0.098874

Small

Yes

Straight

Player

3

395,087,247,768

0.014205

0.042614

Small

Yes

Flush

Player

3.5

190,959,227,136

0.006866

0.024030

Small

Yes

Full house

Player

5

43,297,986,840

0.001557

0.007784

Small

Yes

Four of a kind

Player

12

859,737,984

0.000031

0.000371

Small

Yes

Straight flush

Player

52

1,962,591,576

0.000071

0.003669

Small

Yes

Royal flush

Player

502

42,135,660

0.000002

0.000760

Small

No

Less than straight

Player

1

720,579,458,748

0.025907

0.025907

Small

No

Straight

Player

2

136,018,223,484

0.004890

0.009781

Small

No

Flush

Player

2.5

40,911,000,804

0.001471

0.003677

Small

No

Full house

Player

4

0

0.000000

0.000000

Small

No

Four of a kind

Player

11

0

0.000000

0.000000

Small

No

Straight flush

Player

51

269,696,304

0.000010

0.000495

Small

No

Royal flush

Player

501

6,109,020

0.000000

0.000110

Small

Push

0

418,339,128,088

0.015041

0.000000

Small

Yes

Dealer

-3

2,700,150,685,692

0.097079

-0.291238

Small

No

Dealer

-2

47,223,220,344

0.001698

-0.003396

Fold

-2

5,335,144,079,760

0.191816

-0.383633

Total

27,813,810,024,000

1.000000

-0.021850

The lower right cell shows a house edge of 2.185% per ante bet. What this means, for example, is if you bet $1 and both the Ante and Blind initially, then you can expect to lose 2.185 cents on average. However for comparison to other games I believe the Element of Risk is more appropriate to look at. The average total amount bet by the end of the hand is 4.152252 times the ante bet. So the element of risk would be 2.185%/4.152252 = 0.526%.

Large bettors should be wary of maximum payouts. If your ante bet is more than 1/500 of the maximum payout, then you will get shortchanged on a royal flush. For every 100 the effective payout on a royal goes down, the house edge will go up by 0.308%. In other words, the increase in the house edge will be [500-(MP/500)]*0.0000308, where MP is the maximum payout.

The next table shows the average wager and return from each bet.

Ultimate Texas Hold 'Em® Return Table

Bet Type

AverageWager

AveragePays

AverageWin

Ante

1

-0.165757

-0.165757

Blind

1

-0.314685

-0.314685

Play

2.152252

0.213076

0.458593

Total

4.152252

-0.02185

Wizard Strategy

The following is my "Wizard Strategy" for Ultimate Texas Hold 'Em®.

Large Raise: The following table shows when to make the 4X raise.

Medium Raise: Make the 2X raise with any of the following:

Two pair or better.

Hidden pair*, except pocket deuces.

Four to a flush including a hidden 10 or better to that flush

* Hidden pair = Any pair with at least one card in your hole cards (thus the pair is hidden to the dealer).

Small Raise: Make the 1X raise with any of the following, otherwise fold:

Hidden pair or better.

Less than 21 dealer outs beat you.

Example

What I mean by an "out" is a dealer hole card that will cause you to lose. Let's look at this situation as an example.

In the example above, there 15 cards that will pair the dealer and beat you (three suits each of K, 7, 2, A, and 10). Then there are the two ranks (jacks and queens) which will out-kick the player. All four jacks and queens remain in the decks, so that is 2×4=8 more cards that will beat you. So, we're up to 15+8=23. We don't count the other three nines because those will result in a push. So, because there are only 23 outs (21 or more), we fold.

BTW, using my Ultimate Texas Hold 'Em® calculator, we see that the expected value of raising this hand is -2.136364, which is less than the -2 of folding.

I get asked a lot about combinations of cards that will beat the player. For example, any two dealer spades that would give the dealer a flush in the example above. The answer is no. It would really make things complicated if the strategy accounted for double-card combinations that would beat the player.

Following my Wizard strategy will result in a house edge of 2.43% and an Element of Risk of 0.58%.

The second and third decision points are influenced by the , for which I have great respect, as I do for all of Grosjean's work. I highly recommend his strategy if you want to something even more powerful than my simple strategy above.

Trips Bet

Shufflemaster literature mentions the following four possible pay tables on the Trips bet.

Trips Bet - Pay Table 1

Player Hand

Combinations

Pays

Probability

Return

Royal flush

4324

50

0.000032

0.001616

Straight flush

37260

40

0.000279

0.01114

Four of a kind

224848

30

0.001681

0.05042

Full house

3473184

9

0.025961

0.233649

Flush

4047644

7

0.030255

0.211785

Straight

6180020

4

0.046194

0.184775

Three of a kind

6461620

3

0.048299

0.144896

All other

113355660

-1

0.8473

-0.8473

Total

133784560

1

-0.009018

Trips Bet - Pay Table 2

Player Hand

Combinations

Pays

Probability

Return

Royal flush

4324

50

0.000032

0.001616

Straight flush

37260

40

0.000279

0.01114

Four of a kind

224848

30

0.001681

0.05042

Full house

3473184

8

0.025961

0.207688

Flush

4047644

6

0.030255

0.18153

Straight

6180020

5

0.046194

0.230969

Three of a kind

6461620

3

0.048299

0.144896

All other

113355660

-1

0.8473

-0.8473

Total

133784560

1

-0.01904

Trips Bet — Pay Table 3

Player Hand

Combinations

Pays

Probability

Return

Royal flush

4324

50

0.000032

0.001616

Straight flush

37260

40

0.000279

0.01114

Four of a kind

224848

30

0.001681

0.05042

Full house

3473184

8

0.025961

0.207688

Flush

4047644

7

0.030255

0.211785

Straight

6180020

4

0.046194

0.184775

Three of a kind

6461620

3

0.048299

0.144896

All other

113355660

-1

0.8473

-0.8473

Total

133784560

1

-0.034979

Pay table #3 seen at the Mirage.

Trips Bet - Pay Table 4

Player Hand

Combinations

Pays

Probability

Return

Royal flush

4324

50

0.000032

0.001616

Straight flush

37260

40

0.000279

0.01114

Four of a kind

224848

20

0.001681

0.033613

Full house

3473184

7

0.025961

0.181727

Flush

4047644

6

0.030255

0.18153

Straight

6180020

5

0.046194

0.230969

Three of a kind

6461620

3

0.048299

0.144896

All other

113355660

-1

0.8473

-0.8473

Total

133784560

1

-0.061808

Pay table #4 seen at Shufflemaster TableMax units.

Common Progressive

This is the most common progressive jackpot, in my experience, so I'll title it the "Common Progressive." I used to title it the "Michigan Progressive," when the only known placement was in Michigan, but now it is seen all over the place.

There is just a single bet amount, which can be $1 or $5, depending on the table. The following table shows the probability and contribution to the return for the various wins. Wins are relative to the amount bet and are on a "for one" basis.

Common Progressive

Event

Pays

EnvyBonus

Combinations

Probability

Return

EnvyReturn

Royal flush

100% of jackpot

1000

4

0.000002

0.000000

0.001539

Straight flush

10% of jackpot

300

36

0.000014

0.000000

0.004156

Four of a kind

300

624

0.000240

0.072029

0.000000

Full house

50

3,744

0.001441

0.072029

0.000000

Flush

40

5,108

0.001965

0.078616

0.000000

Straight

30

10,200

0.003925

0.117739

0.000000

Three of a kind

9

54,912

0.021128

0.190156

0.000000

Total

74,628

0.028715

0.530569

0.005695

What the table above immediately shows us is fixed wins return 53.06% to the player. For each additional player at the table, besides yourself, your return goes up by 0.57% from the Envy Bonus.

For a $1 bet, every $10,000 in the meter adds 2.924% to the return. Likewise, for a $5 bet, every $50,000 in the meter adds 2.924% to the return.

The next table shows the break-even point, where the Progressive side bet has zero house edge, according to the bet amount and number of other players (not counting yourself).

Common Progressive

OtherPlayers

$1 Bet

$5 Bet

0

$160,530.53

$802,652.63

1

$158,583.16

$792,915.79

2

$156,635.79

$783,178.95

3

$154,688.42

$773,442.11

4

$152,741.05

$763,705.26

5

$150,793.68

$753,968.42

Small Progressive

Many tables in Las Vegas offer a $1 progressive side bet. The top win is for a royal flush using at least one hole card, which I call a "hidden royal flush." There is also a $100 envy bonus if another player gets a hidden royal. The following table shows the return of the fixed wins only, not counting the envy bonus. It shows a return of 45.68%, before considering the jackpot and envy bonuses.

Small Progressive

Event

Pays

Envy

Combinations

Probability

Return

Hidden royal flush

Jackpot

$100

86,480

0.000031

?

Community royal flush

$1000

$0

4,324

0.000002

0.001539

Straight flush

$250

$0

782,460

0.000279

0.069627

Four of a kind

$75

$0

4,721,808

0.001681

0.126050

Full house

$10

$0

72,936,864

0.025961

0.259610

All other

$0

$0

2,730,943,824

0.972047

0.000000

Total

2,809,475,760

1.000000

0.456827 + ?

The return per $1000 in jackpot is 3.08%. The return for the Envy Bonus is 0.308% for each additional player at the table. So each additional player at the table is worth $100 in the meter.

The next table shows how big the jackpot has to be for the Small Progressive to have exactly a 100% return, or zero house advantage.

Break Even Jackpots

OtherPlayers

Jackpot

5

$17,146.07

4

$17,246.07

3

$17,346.07

2

$17,446.07

1

$17,546.07

0

$17,646.07

Buffalo Thunder Progressive

The Big Progressive tends to be much larger, because the player must flop a royal flush to win it. In other words, the player cannot make use of the Turn and River cards to win the progressive, unlike in the Small Progressive. There is no Envy Bonus. It was seen at the Buffalo Thunder casino in New Mexico.

Buffalo Thunder Progressive

Event

Pays

Permutations

Probability

Return

Player flops royal

100% of jackpot

1037760

0.000002

?

Royal partially on board

5% of jackpot

19717440

0.000029

?

Royal entirely on board

3000

1037760

0.000002

0.004617

Straight flush

250

187790400

0.000279

0.069627

Four of a kind

100

1133233920

0.001681

0.168067

Full house

10

17504847360

0.025961

0.25961

All other

0

655426517760

0.972047

0

Total

674274182400

1

0.502077 + ?

The return for at any given time is 50.19% plus 3.00% for each $10,000 in the meter. For exactly zero house edge, the meter would need to be $165,959.74. I'm told the meter is seeded at $5,000, and 27% of money bet goes towards the meter. Fixed wins are not deducted from the meter. That would make the overall return 77.96%.

Bad Beat Bonus

At the Admiral casino in Liechtenstein there is a Bad Beat Bonus side bet. It pays if either the player or dealer lose with a three of a kind or better. Gaming literature mentions two different pay tables. My analysis of both is below. The bottom line is a house edge of 14.79% on pay table 1 and 20.39% on pay table 2.

Bad Beat Bonus — Pay Table 1

Losing Hand

Pays

Combinations

Probability

Return

Straight flush

7,500

10,300,592

0.000004

0.027776

Four of a kind

500

471,040,512

0.000169

0.084677

Full house

50

8,435,225,376

0.003033

0.151637

Flush

30

19,434,208,592

0.006987

0.209618

Straight

20

18,271,076,976

0.006569

0.131381

Three of a kind

9

64,049,759,448

0.023028

0.207252

Low hand win*

-1

2,557,579,127,088

0.919536

-0.919536

Tie

-1

113,130,263,816

0.040674

-0.040674

Total

2,781,381,002,400

1.000000

-0.147868

Bad Beat Bonus — Pay Table 2

Losing Hand

Pays

Combinations

Probability

Return

Straight flush

10,000

10,300,592

0.000004

0.037034

Four of a kind

500

471,040,512

0.000169

0.084677

Full house

40

8,435,225,376

0.003033

0.121310

Flush

25

19,434,208,592

0.006987

0.174681

Straight

20

18,271,076,976

0.006569

0.131381

Three of a kind

9

64,049,759,448

0.023028

0.207252

Low hand win*

-1

2,557,579,127,088

0.919536

-0.919536

Tie

-1

113,130,263,816

0.040674

-0.040674

Total

2,781,381,002,400

1.000000

-0.203873

*: A "low hand win" is a winning hand of two pair or less.

Hole Card Bonus

I'm told this side bet can be found in Washington state, the Flamingo in Las Vegas, and Norwegian cruise ship casinos. It pays based on the player's hole cards, except the top award also involves the dealer's hole cards. The lower right cell in the following table shows a house edge of 8.54%.

Hole Card Bonus

Bet

Pays

Combinations

Probability

Return

Player and dealer have aces

1000

6

0.000004

0.003694

Pair of aces

30

7,344

0.004521

0.135636

A/K suited

25

4,900

0.003017

0.075415

A/Q or A/J suited

20

9,800

0.006033

0.120664

AK off-suit

15

14,700

0.009050

0.135747

Pair J's - K's

10

22,050

0.013575

0.135747

A/Q or A/J off-suit

5

29,400

0.018100

0.090498

Pair 2's - 10's

3

66,150

0.040724

0.122172

All other

-1

1,470,000

0.904977

-0.904977

Total

1,624,350

1.000000

-0.085406

Australian Rules

I have an unconfirmed report that at the Crown casino in Perth, Australia, the blind bet pushes if the dealer doesn't qualify and the dealer wins. Assuming no change in strategy, this happens 1 in every 176 hands. When it happens, the player will lose one less unit. The effect is a reduction in the house edge from 2.185% to 1.617%.

.

6-Card Bonus

Some casinos add on a side bet known as the 6-Card Bonus. This side bet is found on multiple poker-derivative games, so I created a special page for it. For more information, please see my page on the 6-Card Bonus.

Play for Free

I'm very proud to offer my Ultimate Texas Hold 'Em® game. What I'm especially pleased with is the advice feature, which offers advice based on optimal strategy. Webmaster J.B. worked very hard on this so please have a look.

Heads Up Hold 'Em. Similar game, offering bad beat bonuses, but 3x raise only after two cards.

External Links

— Entry on Ultimate Texas Hold 'Em.

has an outstanding analysis of this game, including what I call his "nut kicker" strategy for the second and third decision points.

Shufflemaster's .

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— Play this licensed demo game at our sister site Latest Casino Bonuses.